During its recent budget deliberations, the New York City Council sought to add 1,000 cops to the NYPD’s present authorized complement of 35,000 officers. But Mayor de Blasio and Police Commissioner Bill Bratton opposed the measure, and it didn’t pass.

Then, as gunfire swept several precincts and some public-housing projects, the NYPD announced that it will assign as many as 1,200 more officers to high-crime areas.

Nearly 600 of them will be rookies who’ve just finished six months of training at the Academy. Several hundred others will be officers previously working on inside assignments.

The Catch-22 is that this exercise in musical chairs doesn’t add one cop to the overall strength of the force, it only moves them around. The patrolmen’s union has labeled the program “a Band-Aid on the 10 percent rise in shootings so far this year.”

A few weeks back, the NYPD said that people shouldn’t worry about the rise in nonfatal shootings because overall murder is down.

That statistic may only indicate that our city’s first-rate medical-emergency-response programs should take a bow for their ability to save gunshot victims who previously would’ve been goners.

And last month Commissioner Bratton observed that “crime goes up and it goes down” as if this were some natural law. That’s not what the NYPD was saying in the 1990s, when it managed to cut the number of murders from well over 2,000 a year to a few hundred.

At that time, the department demonstrated that police can permanently reduce crime.

When some observers suggested that the jump in shootings might be due to the fact that street interrogations are down 89 percent compared to the same period last year, the commissioner stated that there is no relationship between the two.

Now he has backtracked somewhat, saying that the department will conduct a study of the matter though he would be “very surprised if we’re going to show direct correlation between the decline of stop, question and frisk and the sharp, short-term increases in shootings.”

If the study is done in-house, no police official who values his career will wish to embarrass the commissioner by springing an unpleasant surprise.

Some academic studies in other cities have demonstrated a correlation, but they have been ignored, perhaps because they don’t fit the official wisdom.

Someone always is the loser: If Counterintelligence analysts are sent out to patrol the housing projects, for example, their remaining colleagues will have to work longer hours to monitor developments in the exploding Middle East that might lead to terrorism in New York.

The notion that inside cops can easily be replaced by civilians is a myth. The reality is that police officers working on the inside are often performing important tasks that only a veteran cop can carry out.

If we look at the 1980s, we see some similarities between then and now. Back then, the NYPD was chasing its tail and lurching from crisis to crisis.

Not until the Safe Streets Act provided more officers starting in 1991 could the department go on the offensive against gunmen and bring crime way down.

A better way to deal with the current crisis would’ve been to hire more cops in the first place. City officials should swallow their pride and accept the council’s original offer of 1,000 more cops.

Adding that many police slots to a department that has lost over 5,000 in the past decade is a reasonable proposal.

This would leave the NYPD better set to face the next crisis — and there are plenty of them on the horizon, from a revival of the drug wars of the 1980s to increased terrorism, etc.

Then the police won’t have to guess where the hotspots will be, but will have enough strength to saturate problem areas when threats break out.

That’s the old football strategy of “flood the zone.” But if the NYPD can only put 10 players on the field and not the regulation 11, the department will be the one that is flooded.

Thomas A. Reppetto is the former president of the Citizens Crime Commission of New York City and author of “American Police: 1945 To 2012.”